Hypotheticals are really fun. They let people dream about scenarios that real life doesn’t permit (what a stickler). You can use magic to just make things happen, you can assign any attribute to any thing, and most importantly, you have the freedom to mess around.
The best way, I think, to use that freedom is to put a plain old apple in a magical indestructible box, and let it drift through intergalactic space. At first, you’d feel a sense of great disappointment. You had the power to do ANYTHING and you’ve wasted it on an apple. In reality though, you kinda did create ANYTHING.
That apple, in that box, will eventually become everything that ever was, and ever can be. Just with enough time. The idea that something can become anything is related to a concept known as the “Boltzmann Brain.” Coined by modern cosmologists and philosophers building upon the work of 19th-century Austrian physicist Ludwig Boltzmann, it suggests that the odds of a conscious brain spontaneously forming in a random, high-entropy universe are greater than the odds of complex life evolving gradually from low-entropy beginnings.
Boltzmann was a pioneer in statistical mechanics, the field that connects the microscopic behavior of particles with the macroscopic laws of thermodynamics. His most famous equation, S = k log W, relates entropy (S) to the number of possible microscopic configurations (W) that correspond to a macroscopic state. In simpler terms, entropy measures disorder, or how many ways you can rearrange the components of a system without changing what it looks like overall.
A vase of flowers is an ordered system. The same vase, shattered on the ground, is disordered. And in a world governed by the second law of thermodynamics, systems overwhelmingly tend to evolve from order to disorder. That’s why vases break but don’t un-break. Left alone, the pieces of the vase will scatter, the flowers will decay, and the water will evaporate. The system moves toward higher entropy.
But (and this is key) statistical mechanics doesn’t make that outcome inevitable. It only makes it vastly more probable. Given enough time, the opposite could happen. It’s not physically impossible for the atoms of a shattered vase to reassemble themselves into a pristine vase again; it’s just incredibly, unfathomably unlikely. But if the universe is infinite, or lasts infinitely long, then every possible arrangement of atoms will occur. Not just once, but an infinite number of times.
And that brings us back to the apple in the box. Over time, the apple will rot. The molecules will break down. The whole system becomes increasingly disordered. But with infinite time, the atoms of that apple can (by sheer chance) rearrange into a banana, a pineapple, or even a brain. A brain with false memories, a fake identity, and a hallucinated universe all its own. That’s the crux of the Boltzmann Brain paradox. It raises an unsettling question: If random brains are more statistically likely than orderly cosmic histories like ours, then shouldn’t we expect to be one of those random brains?
Let’s back up. Before I reduce you to just your head, let’s understand how this works. Entropy almost always increases. That’s not a hard rule of nature, but a statistical truth. Boltzmann’s genius was to recognize that the direction of time is linked to the increase of entropy. In a low-entropy early universe, like the one after the Big Bang, there were few ways for matter to be arranged. As time passes, those possibilities explode. Systems become messier, more random. But with infinite time and space, even the lowest-entropy states will eventually reoccur. Not because the universe has a purpose, but because probability insists that, given enough rolls of the dice, everything that can, will happen.
The Boltzmann Brain problem plagues modern cosmology. If a single disembodied brain floating in space is more probable than the entire evolutionary chain that produced humans on Earth, then how can we trust our memories, our observations, or even our sense of time? Every philosophical theory about consciousness, perception, and even ethics is forced to assume, with no proof, that we’re not just brains that flicker into existence for a moment and disappear.
The theory can get really deep because infinity is a dangerous thing. With infinite time, even the most niche, unlikely thing is BOUND to happen. The atoms of our apple separate and combine in infinite different ways at infinite different times, and they can truly become anything.
The Boltzmann Brain paradox is a testament to how truly wild statistics are. The odds of an elephant riding a unicycle with a party hat appearing at your front step are exceedingly low, almost zero. But not quite zero. With infinite time, everything that is not 0 full stop, will happen.
Now I bet you’re not as disappointed as before! That apple really has potential.
So, are we just brains floating around in space? The odds of that aren’t 0, so the answer is maybe. But it is far more exciting and hopeful to just assume that we are not. In reality, we cannot sit idly by for eternity waiting for that apple to turn into a brain, and if we could, the same processes that disorder the apple would disorder us too. Still, hypotheticals remain fun to think about, because they represent something new.
So, dream up hypotheticals! Work out your (hopefully non-apple) Brains!
– Vihaan Anand Eswarapu
